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- Eriksson, Henrik, et al.
(författare)
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Expected inversion number after k adjacent transpositions
- 2000
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Ingår i: Formal Power Series and Algebraic Combinatorics. - 3540672478 ; , s. 677-685
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Konferensbidrag (refereegranskat)abstract
- We give expressions for the expected number of inversions after t random adjacent transpositions have been performed on the identity permutation in Sn+1 The problem is a simplification of a problem motivated by genome evolution. For a fixed t and for all n greater than or equal to t, the expected number of inversions after t random adjacent transpositions isE-nt = t - 2/n ((t)(2)) + Sigma(r=2)(t) (-1)(r)/n(r) [2(r)C(r)((t)(r+1)) + 4d(r) ((t)(r))]where d(2) = 0, d(3) = 1, d(4) = 9, d(5) = 69,... is a certain integer sequence. An important part of the our method is the use of a heat. conduction analogy of the random walks, which guarantees certain properties of the solution.
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